help-10

[twilit meteor]

nice

[timid silo]

yeah

pretty smart huh

👏

asian ?

[twilit meteor]

btw are u a jee aspirant?

[timid silo]

💀

[twilit meteor]

my queston prolly answered urs

[timid silo]

bhai ye dekh ke samaj gaya tha vese bhi

😂

[twilit meteor]

lol

[timid silo]

jee wale hi essa binomial approximation karte hai

teachers bhi padhate vese hai :/

[twilit meteor]

true

ur 12th or 11th

[timid silo]

any guess ?

[twilit meteor]

12th

[timid silo]

bruh how ?

[twilit meteor]

11th grader wudn't know IBP

but u m8 be a guy who already wrote jee last yr

[timid silo]

🤔 which coaching

[twilit meteor]

allen. wbu?

[timid silo]

ho gaya hai mera lol

no coaching

[twilit meteor]

whch year

[timid silo]

kota ?

last

[twilit meteor]

no no im not that stupid

[timid silo]

😆 btw 11th me int ?

[twilit meteor]

how much did u get in mains

[twilit meteor]

yea

not bad. tbh

[timid silo]

bruh any guess ?

[twilit meteor]

teeachers are pretty good

[timid silo]

good

[twilit meteor]

idk bro after this years mains predictions mean ntg

[timid silo]

it was just bad giving this year again 💀

[twilit meteor]

250 marks gettng just slightly more than 99 percentille

[timid silo]

i messed up

[twilit meteor]

u took drop ah?

[timid silo]

solved integers and ruined

its just depressing ugh

anyways gonna get 99 atleast this time for sure

[twilit meteor]

wdym

[timid silo]

nothing long story xd

[twilit meteor]

ATB bro

[timid silo]

yeah

you done with trigono ?

ofc ig

[twilit meteor]

yea but prolly dont remember shit

[timid silo]

go check out #help-12

posted a problem myself

[twilit meteor]

sure

[timid silo]

close this one

[twilit meteor]

.close

[obtuse pebble]

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[obtuse pebble]

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[terse obsidian]

does anyone know how they got di² in this correlation task?

[terse obsidian]

i dont know how to get di² in this.

: (

<@&286206848099549185> idk how to describe my problem better if thats what is keeping people from answering. if you need more infos from me i can give them. I basically have the problem that i dont know how they got that di² in the screenshot. the 1, 16 and 0. its from my statistik class

[timid silo]

@terse obsidian egonimo more like ni||gomino||

[terse obsidian]

?

so i have these tabels for corellation questions. and before i need to get stuff like Pearson's correlation coefficient i need to get di²

[timid silo]

If u send me ur pfp I will solve problem for u

[terse obsidian]

nevermind i found out. dont need you with your shitty jokes

.close

[obtuse pebble]

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[snow meteor]

can you help me with some math ? i dont understand and i need it quickly

[rotund bolt]

what is it?

[versed stratus]

need it quickly

why

[snow meteor]

where i can show you this ?

[versed stratus]

what's the rush?

[snow meteor]

im doing my homework and i cant do this , i tried like 20 times and it just wrong answer

please i really need it

[rotund bolt]

you can send a picture of the question or type it

[snow meteor]

sure

[rotund bolt]

picture preferred

[snow meteor]

i dont understand this

[rotund bolt]

wtf is this

[snow meteor]

i dont know my math teacher did that

[versed stratus]

You're missing a lot of brackets

[snow meteor]

thats the question i asked myself

they said its "two fraction digits"

or sum

[rotund bolt]

did he just send you this?

[snow meteor]

different shit

[snow meteor]

yes

thats stupid

if you answer this for me i will give you bułka

are you there ?

[rotund bolt]

solving this without brackets

is stupid

[snow meteor]

can you even try that in your way?

if its possible?

[rotund bolt]

the 2 consecutive "/" are killing me

[snow meteor]

its like i gues

guess*

wait

[obtuse pebble]

@snow meteor Has your question been resolved?

[obtuse pebble]

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[vast echo]

struggling with this a lot, i tried getting y and z in terms of x and r and plugging that into the arithmetic series but that gives me a series of 2 equations with 3 unknowns and im not sure if thats possible

[vast echo]

the book gives this hint which seems to suggest using some kind of substitution but i cant see how to make it work

<@&286206848099549185>

[minor nexus]

Write your equations

[vast echo]

x + d = 2xr
x + 2d = 3xr^2

been playing around with these but i cant figure out how to get r

wait i have an idea

i might have 0 = 3xr^2 - 4xr - 2x but i dont think that helps either

wait i have something

nvm that doesnt work

[brittle topaz]

here you can divide by x since x not = 0

[vast echo]

oh true

i didnt notice that

[rotund bolt]

if x , 2y , 3z is an Arithmetic sequence , 2y-x = 3z-2y

=> 4y = x+3z

x , y , z is a Geometric sequence

y = rx , z = r^2x

4rx = x +3r^2 x

x gets cancelled out

you have a quadratic in r

r = 1 , 1/3

[brittle topaz]

dont post solutions

[vast echo]

i dont think thats correct

[rotund bolt]

hm?

[vast echo]

1 isnt at least

since x != y

[minor nexus]

Can you verify?

For example if I wanted you to be more fancy, can you tell me for what x you can use? Can you verify your solution(s) for r?

[vast echo]

?

[rotund bolt]

ye then it's 1/3 , sorry I didn't read that x!=y

[vast echo]

i think i got 1/3 with a slightly different answer

i got d = 2xr - x, so -x + 4xr = 3xr^2, divide by x and thats the same quadratic

[rotund bolt]

I got the same quadratic

[minor nexus]

None of that is surprising because similar logic should lead to similar conclusions

Both of you are using the same basis, AP and GPs

[minor nexus]

But if there are any doubts, this should be answered

[rotund bolt]

all of that would lead to the same place

we're gonna end up with the same quadratic

[vast echo]

.close

[obtuse pebble]

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[strange fiber]

.

[strange fiber]

Can anyone explain to me

how is this step crucial?

<@&286206848099549185>

[errant hemlock]

Any math problems we can solve together?

[obtuse pebble]

@strange fiber Has your question been resolved?

[tardy epoch]

It's used in the lines below it

[obtuse pebble]

@strange fiber Has your question been resolved?

[obtuse pebble]

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[regal sequoia]

Can someone check my proof

[regal sequoia]

Is it accruate

[obtuse pebble]

@regal sequoia Has your question been resolved?

[obtuse pebble]

@regal sequoia Has your question been resolved?

[low ravine]

<@&286206848099549185>

[hollow glacier]

EF and DF should be (sqrt(2) x a) and rest of the proof is correct

as you calculate ED it is 2a

[obtuse pebble]

@regal sequoia Has your question been resolved?

[regal sequoia]

Okay thabks

[obtuse pebble]

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[next magnet]

hello

[next magnet]

trying to solve this problem

turning quadtratic to standard form

what do i do with the -3x when i factor?

[static furnace]

probably should've factored it out beforehand no?

[next magnet]

I am watching yt vid on how to do it

Sorry didnt mean to tag

Just natural to “reply” to ppl

[static furnace]

no you're good. you replied to my comment

[next magnet]

But im kinda just following how he did it in examples

[next magnet]

Shoulda told that to the other guy who lost his beans over me tagging him in a reply ☠️

Do u have a vid u’d recommend or maybe if ur able to walk me through?

[static furnace]

are you trying to put it into vertex form?

a(x-h)^2+k?

[next magnet]

Yes

[static furnace]

okay so from the very beginning of the problem then I would first start by factoring out the coefficient of x

proceeding how you normally would from there will get you where you need to be

[next magnet]

Okay i’ll try

[static furnace]

alright let me know what you get

[next magnet]

Dude i had a pre calc exam on Thursday and i think i failed

Might have to drop the course ..

[next magnet]

Im a lil preoccupied gimme 10 mins or so

[static furnace]

no worries

[next magnet]

ok lemme get cracking at this shit

[next magnet]

im sorry what exactly does this mean

[static furnace]

so factor out 3 from (3x^2+24x)

the number in front of the x^2 is its coefficient

we dont want a coefficient directly in front of x in standard form

[static furnace]

but it is normal to have one outside of the parentheses as seen here

[next magnet]

uh

okay holdon

[static furnace]

i'll try to find you a video too

[next magnet]

nah i got it now

so it would be

x^2+8x-16

then i do what i was doing before

so

(8/2)^2 then +16-16 to the equation

[static furnace]

well you currently should have something like -3(x^2+8x+16-16)-48 right?

[next magnet]

and solve

i dont have the -3

[static furnace]

oh

[next magnet]

i tht when we divide the 24 and 48 by -3 it cancels it?

[static furnace]

you're not trying to cancel anything, just moving things around

[next magnet]

hm

okay

[static furnace]

that -3 becomes a in this

so factoring it out gives you -3(x^2+8x)-48 right?

[next magnet]

yeah

wait

[static furnace]

okay so then you "perfect square" the inside

[next magnet]

how does the 48 stay???

[static furnace]

it's not inside the parentheses

[next magnet]

oh

so

im only focusing on

oh shit

wait

oops i see now

[static furnace]

lol

[next magnet]

shouldnt this be -3(x^2+8x-16)-48

or is it bc u already did the +16-16

[static furnace]

the +16-16 was the next step. the 16 isn't there naturally

[next magnet]

i gotcha

okay

[static furnace]

so basically from here, you need to make (x^2+8x) a perfect square. just focus on that part

[next magnet]

so now i just factor 8x - 48?

[next magnet]

nvm i see wym

shit

dude

i suck at this wtf

[static furnace]

nah you don't suck at this

just takes practice

What do you get inside the parentheses? Don't simplify anything yet

[next magnet]

holdon im gonna run out real quick

is this chat gonna close

i'll try to like text so it stays active

[static furnace]

If it closes, I'll reopen it

But I've seen channels open here for a full day as long as you respond to the bot so

And if no one responds, including me, feel free to dm me

[iron edge]

[obtuse pebble]

@next magnet Has your question been resolved?

[next magnet]

Thank you sir

Im active otp !!

[next magnet]

okay

so

as it stands

i have

-3(x^2+8x)-48

[next magnet]

hi @static furnace sorry dont mean to be annoying

[obtuse pebble]

@next magnet Has your question been resolved?

[next magnet]

no

sigh

[static furnace]

yea so -3(x^2+8x) needs to be turned into a perfect square

how would you go about doing that

@next magnet

[next magnet]

Im not sure, idk what i need to distribute

[static furnace]

you dont need to distribute anything yet

just make x^2+8x into a perfect square

so (8/2)^2=16 right

so -3(x^2+8x+16-16)-48

[static furnace]

the -48 coming from the original

following so far?

[next magnet]

Yeah hold on im sorry

[next magnet]

okay yes

following

i got it

but idk what im supposed to do with

-3(x^2+8x)-48

[static furnace]

what happened to the +16-16?

[next magnet]

well

once i solve for whats inside paranthesis doesnt it just cancel out?

[static furnace]

but i put them there to make a perfect square

[next magnet]

okay

holdon then

[static furnace]

you see what i'm saying?

[next magnet]

yeah

so is

+16) - 16 -48

right?

[static furnace]

no

have to add/subtract them inside the parentheses

[next magnet]

entire thing in ()?

ohhhh

okay

now we are on same page

[static furnace]

okay so -3(x^2+8x+16-16)-48
then -3((x^2+8x+16)-16)-48
and -3((x+4)^2-16)-48

is that legible? i can send it through a bot to make it look cleaner

[next magnet]

no thats good

hold

okay got it

[static furnace]

alright so from here, simplify

without expanding the exponenet

[next magnet]

so -16 - 48

[static furnace]

what about -3

[next magnet]

divide?

[static furnace]

from the last equation

multiply the -3 to both factors in the parentheses

[next magnet]

uh

right

wait

ohhhh

ok ok i see

holdon

brain is slow rn

so it should be

-3x+4^2-16+144

[static furnace]

you forgot parentheses somewhere

but i dont think thats it

should have -3(x+4)^2-3*(-16)-48

[next magnet]

dont i factor -3 ((x+4)^2 - 16) then -3(-48)

[static furnace]

-3*-16?

[next magnet]

i tht that was already in w the x+4

[static furnace]

hmm?

[next magnet]

so now

i have

-3x+4^2-48-48

[static furnace]

parentheses?

where's your perfect square?

remember we want it in the form a(x-h)^2+k

[next magnet]

oh wait

-3(x+4)^2-48-48

meant to do that

woops

so then

i do

-48 - 48

which would be

+48

so

-3(x+4)^2+48

cengage just said im wrong....

gonna go fuck myself

[static furnace]

when you multiply the -3 by the -16 what do you get

[next magnet]

48

[static furnace]

right and 48-48 is

[next magnet]

0

[static furnace]

mhmmmm

[next magnet]

oh shit

ima kms

[static furnace]

standard form

[next magnet]

right

standard form

i tht the + k
would cancel out

[static furnace]

hmmm

[next magnet]

chat gpt

gave this

[static furnace]

do not use chat gpt

[next magnet]

o

uh

yeah

right

lmaooooooo i am trying not to anymore

but anywho chat gpt got it wrong too

i actually wanna learn man

i enjoy math

but not this math

i like finance related stuff

[static furnace]

i know where we went wrong

where I went wrong

[next magnet]

i went wrong when my parents decided to have me

[static furnace]

when I factored out a -3 in the very beginning I forgot a negative

should've been -3(x^2-8x)-48

not +8x

you see what i mean?

[next magnet]

okay one sec

yeah

im gonna

restart

from top

gimme min

[static furnace]

we originally had (-3x^2+24x)-48

taking out a -3 would give us -3(x^2-8x)-48

from there we go about the same way we did originally

but one of our +'s is now a -

[next magnet]

Look right?

-3 (x-4)^2

[static furnace]

as long as that second to last line is +48-48 yes

yep!

[next magnet]

it was -48

[static furnace]

-3*-16

[next magnet]

right

positive

okay

so wait

okay

i see

bruh i j got logged out of cengage

[next magnet]

its right

we good w that now

thank god

thank you

bro

really appreciate it

[static furnace]

yeah no problem!

[next magnet]

so

would the axis of symmetry be 4?

[static furnace]

what is the vertex

[next magnet]

or does the vertex become the opposite of x

so

4,0

[static furnace]

yes

[next magnet]

so

axis of symmetry

would

be 4?

[static furnace]

what is 4

[next magnet]

x = h

[static furnace]

so x=4

[next magnet]

hm

[static furnace]

yes

[next magnet]

why is

cengage

saying

wrong

[static furnace]

y=4

[next magnet]

if x = 4

since

x = h

why

is

it y

[static furnace]

the vertex is (4,0)

[next magnet]

ohhhhh

no

[static furnace]

no?

[next magnet]

cengage still saying wrong

[static furnace]

it says (4,0) is wrong?

[next magnet]

i put

y = 4

and it said wrong

[next magnet]

and this is wrong

i hate cengage

[static furnace]

that's odd

standard form is a(x-h)^2+k, where (h,k) is the vertex

[next magnet]

wouldnt it be

(0,4)

[static furnace]

would it?

[next magnet]

no clue

still wrong

i give up man

[static furnace]

im looking at a graph of it right now and it's (4,0)

[next magnet]

why is cengage saying its wrong then wtf

[static furnace]

unsure. but it says that your equation is correct so

[next magnet]

yeah

idk

[static furnace]

at least there's that

[next magnet]

thank you again bro

[static furnace]

we're not crazy

i promise

[next magnet]

im gonna continue this tmr 🙏

[static furnace]

anytime

good luck!

[next magnet]

appreciate the help

i was genuinely rlly struggling w this

[static furnace]

hopefully i helped!

.close

[obtuse pebble]

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[fathom kindle]

how do i simplify this

the answer is 13√2 but i dont get how

[dusk widget]

are you familiar with the rule that sqrt(ab) = sqrt(a)*sqrt(b)?

[fathom kindle]

yes

[dusk widget]

okay

[fathom kindle]

i just learned it

[dusk widget]

so the issue is this sqrt(32)

[fathom kindle]

ya but its connected to 4

[dusk widget]

let's use this fact to make it nicer

what can we factor 32 into?

[fathom kindle]

16 and 2

[dusk widget]

ok

then sqrt(32) = sqrt(16)*sqrt(2)

what is sqrt(16)?

[fathom kindle]

4

[dusk widget]

right

[fathom kindle]

so its 4√2

[dusk widget]

so 4sqrt(32) - 3sqrt(2) = 4[4sqrt(2)] - 3sqrt(2) = 16sqrt(2) - 3sqrt(2)

and you have your answer!

does that make sense?

[fathom kindle]

wait so what about the very start

the 4 at the begining

because instead of 4√32 it changed to 4√2 (which I understand how we got the 4√2)

[dusk widget]

ah so

sqrt(32) = 4sqrt(2)

[fathom kindle]

righttt

[dusk widget]

so then 4sqrt(32) = 4[4sqrt(2)]

[fathom kindle]

i see

ok thank you!

.close

[obtuse pebble]

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[late zephyr]

I understand the derivation leading to the memoryless property, but I cant seem to understand its application in a real scenario.

Let say we have a period $P$, in which no event occurs, if the memoryless property is true, it seem to me that the probability that an event occur at any instance $i$ in $P$ is a constant.

The memoryless property is defined as:
$$\mathbb{P}(T> s+t \vert T > s) = \mathbb{P}(T> t)$$
In case of that $t$ is approaching $0$ (i.e the very next instance).
$$\mathbb{P}(T> s+0 \vert T > s) = \mathbb{P}(T> 0)$$

Meaning, the probability that an event occurs in the very next instance equal to the probability that an event occurs the very next moment after initial time. And you can do the same thing for every instance $i$ during $P$.

Meaning, during period $P$ in which no event occurs, the probability of an event occur in any instance $i \in P$ is equal to $\mathbb{P}(0)$.

If that is true, why even has a CDF or PDF, as the value is equal to the CDF at time $0$ anyway.
This has been bugging me several days now, can someone explain it to me ?

[warm shale]

andy

[vague spindle]

I may be misunderstanding your confusion, but you seem to be unclear on what CDFs over time tell us; they are the probability that an event has happened by now starting from some initial time. Thus "cumulative" probability. So if we have constant probability density, our CDF is increasing.

[late zephyr]

Sorry i meant the PDF in my last sentence

[vague spindle]

ah

well the PDF just retains its value

However, over time, as the CDF increases, it eventually hits 1; and by that time the event has to have occurred

So it cannot continue past that

[late zephyr]

yeah, but considering period $P$ in which no event occur. The memoryless property seem to suggest that the probability of event occuring at any instance $i$ is the same. Which seem weird to me.

[warm shale]

andy

[vague spindle]

It's a bit fallacious to think about the PDF telling us about instantaneous probability

The probability of an event happening at an instant is always 0

[late zephyr]

yeah that why i used probability, not PDF

[vague spindle]

But there is no probability of an event occurring at an instant...

There is only the probability of an event occurring during an interval

[late zephyr]

okay what if the interval is very very small

[vague spindle]

There's still a probability, just a very very small one (unless of course the PDF is very very large in that interval)

Are you familiar with integral calculus?

[late zephyr]

yeah

[vague spindle]

The probability of an event happening during an interval is the integral of the PDF with respect to time over that interval

[late zephyr]

i meant if i chop the periof $P$ into various interval $i$. The memoryless property seem to suggest that the probability of event occuring in all these invertal $i$ is the same

[warm shale]

andy

[vague spindle]

That is only true if all the intervals are of the same length

[late zephyr]

Yes

that is what i'm saying

small and the same length interval

[vague spindle]

Well, you can chop it up into a lot of small intervals...

[late zephyr]

am i missing something here ?

[vague spindle]

Possibly...

What exactly is confusing you

[late zephyr]

okay

ima state my logic again line by line

tell me if i get anything wrong

[vague spindle]

alright

[late zephyr]

Memoryless property: waiting does not help, the probability of an event occuring during some interval $s$ does not depend on its past, given that the event hasnt occured in the pass

[warm shale]

andy

[late zephyr]

Given a period $P$, chopped into various interval $i$, whose length approching $0$

[warm shale]

andy

[late zephyr]

Let $s$ be some time between $0$ and $P$.

[warm shale]

andy

[late zephyr]

the memoryless property suggest: $P(T > s + i \vert s) = P(i)$

[warm shale]

andy

[vague spindle]

ohhhh i see your confusion here

you're thinking of the PDF as unchanging

[vague spindle]

However, this has a conditional; it's the probability given that it hasn't happened yet

meaning we are constantly updating the PDF to account for the fact that it has not yet occurred; which makes sense as a "memoryless property" if you look at the PDF as scrolling past a fixed playhead (the current time) rather than a playhead moving across the PDF

[late zephyr]

Does that also meant $P(T> s + 2i \vert T > (s+i)) = P(i)$

[warm shale]

andy

[late zephyr]

yeah you get what I'm saying right

its constant given that an event has not happened

[vague spindle]

yes

[late zephyr]

does that feel weird to you ?

its fucking weird man

[vague spindle]

It's a little counterintuitive

Probability is pretty wacky tbh

[late zephyr]

yeah, maybe i shouldnt have given it the condition "had not happended"

[vague spindle]

But it can also make sense; think of it as you're constantly stuck at t=0

[late zephyr]

yes

that was what i was saying

[vague spindle]

Right now, we can expect events in the future to follow this PDF

But in two seconds, we will expect events in the future to follow the PDF shifted over by 2 seconds, assuming nothing happens

This is a bit of a Bayesian way of looking at it; that probability is the level to which you expect something to happen

[late zephyr]

okay okay, so you also agree that the is no loop hole in my initial proposition right

yeah after the first event happen, it kinda make sense

[vague spindle]

yeah your initial proposition is fairly correct, i think the confusion was how you were looking at PDFs as fixed

or at least intuitively expected them to be

does it make more sense now?

[late zephyr]

I understand PDF and CDF just fine. It just a bit weird when thinking about the interval before the first event happen.

so i brought that cursed intuition to this forsaken land.

anyway, thanks man.

[vague spindle]

anytime

[vague spindle]

yeah, probability and intuition do not get along...

[obtuse pebble]

@late zephyr Has your question been resolved?

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[chilly scroll]

a dice thrown three times chance that sum of three numbers appearing is less than 11

[chilly scroll]

so whatim doing

[late zephyr]

how many faces ?

[chilly scroll]

6

im

Calcing when sum is

11 12 13 14 15 16 17 18

[late zephyr]

dont do that

[chilly scroll]

yea

im getting a series like

10c2 + 11c2 + 12c2 + 13c2

idk how to sum these

[late zephyr]

hmmm

let start with your approach first

what 10c2 ?

[chilly scroll]

okay

45

[late zephyr]

no, i meant what does it meant

[chilly scroll]

oh

mb

I took

x+y+z = 11

then i gave

111

So i can use the

Bars formula

Thingy

n+r-1Cr-1

[late zephyr]

you know latex ?

[chilly scroll]

x+y+z=8

latex!

?

idk

what's that

[late zephyr]

to write mathematic like this $\mathbb(P)(X)=1/2$

[warm shale]

andy

[chilly scroll]

oh this bot

[late zephyr]

did you write down your approch on the paper

[chilly scroll]

yes

[late zephyr]

you can capture it and send it to me

[chilly scroll]

yea hold

this is just roughly what im doin

[late zephyr]

why x+y+2 ?

you assuming one roll will be 2 ?

[chilly scroll]

nono

that's z

[late zephyr]

okay

x+y+z = 11 , what does that meant ?

you trying to find number of cases where the sum of the rolls is 11 ?

[chilly scroll]

oh wait

Yeaaah

Damn

It just hit

rip

[late zephyr]

you need any help with the rest ?

its just counting

[chilly scroll]

ye this is plain wrong

how do i do

[late zephyr]

okay

let answeer this first

ill write down 3 number, which is 3 of my rolls

so the first roll i got is 443

the second roll i got is 344

does they count as the same roll ?

[chilly scroll]

same thing

[late zephyr]

okay

you familiar with Set ?

[chilly scroll]

yes

[late zephyr]

okay what is the set of possible value ?

[chilly scroll]

6^3

[late zephyr]

you sure ?

[chilly scroll]

is it not

[late zephyr]

i dont know haha

[chilly scroll]

[late zephyr]

okay let count the case in which the sum is 3

[chilly scroll]

216 is right ithink

[late zephyr]

only 1 case right {1,1,1}

[chilly scroll]

yes

[late zephyr]

how many if the sum is 4 ?

[chilly scroll]

oh damn

3?

[late zephyr]

does {1,1,2} and {2,1,1} different ?

[chilly scroll]

aah

[late zephyr]

if they are the same then there only 1 case

[chilly scroll]

I think if you see it

Pnc way the order does matter

but the qn just meeds the sum to be 11

So ig that way it counts 1

[late zephyr]

i dont know your problem, i just trying to set you on the right track

now

[chilly scroll]

o

[late zephyr]

Let assume

the first roll is 1

[chilly scroll]

ye

[late zephyr]

so for the two rolls: there sum will be from 2->10 right ?

[chilly scroll]

Can be 12 11 too?

[late zephyr]

no

becasue it have to be less than 11 total

[chilly scroll]

oh ye

okay

[late zephyr]

okay for 2 dices, can you calculate the probability of its sum equal 2 ?

[chilly scroll]

1/36

[late zephyr]

it sum equal 3

[chilly scroll]

or wait

1/18

[late zephyr]

and from these, can you count the number of occurences, in which the first roll is 1, sum with the other two less than 11 ?

[chilly scroll]

Imma try

[late zephyr]

okay

there is a pattern

just take it very slow

write it down

you'll see

[chilly scroll]

@late zephyr also is there a formula for that series

[late zephyr]

im not aware of that, im just counting cases here

[chilly scroll]

Sigma Rc2

I come across a lot

oh

[late zephyr]

my hints is, count the number of cases so that two dices sum up to a certain number, then for each value of the third dice. Sum it with the acceptable number of cases in the two dices.

remember to multiply by 3, as the third dice can be anywhere in the sequence

if you want to use undergraduate formula, look up multinomial distribution

But I want to help you build an intuition before using formula.

[chilly scroll]

damn thanks ye

@late zephyr i found no of cases

For 2 rolls

sum

From 2 to 10

[late zephyr]

okay, so let assume that the third roll is 1

how many case we got for it ?

[chilly scroll]

19

But

[late zephyr]

sum = 2, sum =3, ..., sum =10 right ?

[chilly scroll]

yes

For 2s

Do we permute them too

Cuz if yes

Then its just messy

[late zephyr]

try it

[chilly scroll]

if there's a repition

i would have to

[late zephyr]

yup there are formula to delete these repititions

for example in case of sum of two dice

equal 2 we got 1 case right ?

equal 12 we got how many ?

[chilly scroll]

1 ye

[late zephyr]

equal 3 and equal 11 ?

[chilly scroll]

22

2,

[late zephyr]

equal 4 and equal 10

its like it symmetric right ?

[chilly scroll]

3

oh yea

[late zephyr]

this is what called a normal distribution

[chilly scroll]

ahh

[late zephyr]

https://www.youtube.com/watch?v=zeJD6dqJ5lo

watch this later

now let go back to our problem

[chilly scroll]

okok

[late zephyr]

which sum have the most cases (two dice)

[chilly scroll]

7

6 cases

[late zephyr]

is it symmetric with the center at 7 ?

[chilly scroll]

ye ig

2+12/2

[late zephyr]

-1

anyway

[chilly scroll]

[late zephyr]

continue

[chilly scroll]

is it not?

[late zephyr]

its 2+12/2 -1

[chilly scroll]

Oh i meant

(2+12)/2

[late zephyr]

okay

[chilly scroll]

yeye

[late zephyr]

let step back form our problem a bit

how many number are between the interval 1-10 contain

only integer

10 number right ?

[chilly scroll]

Ye

[late zephyr]

but 10 -1 equal 9 ?

you gotta plus 1

[chilly scroll]

Ye

[late zephyr]

you see your hand

let number the your finger 1 to 5

how many gap do you got ?

[chilly scroll]

yes i know that rule for counting we subtract the extreme and add 1 rigg

[late zephyr]

the interval and the actual 'mark' is a bit different

[chilly scroll]

Oh

[late zephyr]

on your hand, there is 5 number

[chilly scroll]

yes

[late zephyr]

but 4 interval right ?

[chilly scroll]

interval?

[late zephyr]

the gap between your finger

[chilly scroll]

Oh yes

yes

ah so thats

[late zephyr]

this

that why you +1 and -1 in some calculation

[chilly scroll]

Icic

[late zephyr]

you can ponder that later

let get back to our problem

[chilly scroll]

okay

[late zephyr]

if the thrid roll is 1

you sum up the cases for 2-10 right

thrid roll is 2

you sum up for 2-9

[chilly scroll]

Yesyes

ic

[late zephyr]

oh less than 11

mb

thrid rolls 1
you sum up for the cases 2-9

[chilly scroll]

ok

[late zephyr]

thrid rolls 2
you sum up for the cases 2-8

do the same thing for all third roll

and sum them all up

[chilly scroll]

ok wait

[obtuse pebble]

@chilly scroll Has your question been resolved?

[obtuse pebble]

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[blissful bane]

is the reason rolle’s theorem requires continuity on closed interval [a,b] is to have extremum value property of continuous functions on compact sets?

[blissful bane]

like we can always guarantee existence of maximum/minimum with in the set unlike (a,b)

<@&286206848099549185>

[fathom flicker]

Do you have a proof of Rolle's theorem?

[obtuse pebble]

@blissful bane Has your question been resolved?

[blissful bane]

@fathom flicker yes my proof uses extremum value theorem of compact sets and interior extremum value

[fathom flicker]

Well then there you have it

Examine what would go wrong in the proof if there was not guaranteed an extreme value

[obtuse pebble]

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[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
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[summer sentinel]

!status

[obtuse pebble]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[summer sentinel]

3

my answer is 0.1

their given answer is 10.09

[ember frost]

how did you arrive to your answer?

[summer sentinel]

I find the original blood value

then the new blood value

[ember frost]

what was the original blood value?

[summer sentinel]

60/11

[ember frost]

what was the new blood value?

[summer sentinel]

6

[ember frost]

so how did you find the percent change?

[summer sentinel]

i used the formula

(new-old)/old

<=> (3-60/11)/60/11

=0.1

[ember frost]

hm, it is 0.1 indeed

but the question asks for the percent

not the ratio

so what do you do?

[summer sentinel]

times 100?

[ember frost]

yes

so it would be 10%\

[ember frost]

the reason they gave this answer was because they didnt use 60/11 as its initial value

but rather its rounded-to-two-decimal-places value: 5.45

hence, 10.09%

[summer sentinel]

OHH

wow

i DID NOT expect that

[ember frost]

the more you know

since the problem asks the value be rounded to two decimal places, i suggest you obey it and dont use 60/11

[summer sentinel]

thanks for your help

.close

[obtuse pebble]

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[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[fathom flicker]

I have a question about my proof for this because it feels wrong but I can't find any issues

Let v1, ... vn be a basis of V since it is finite-dimensional, and let 1 be a basis of F.

Then I have a theorem that says there exists a unique linear map phi:V->F such that
phi(v_i)=w_i

and in this case since there is only one w_i and it is 1, we have a unique linear map phi:V-<F such that
phi(v_1)=1

So, my proof states that since v is non-zero, we can use it as the first basis vector of V, so letting v_1=v, and we can extend this to a basis

so we have phi(v)=1

Does that work?

[dense imp]

can I ask some questions about this since I haven't taken LA since the age of dinosaurs? :p

[fathom flicker]

Sure

[dense imp]

what is V' ? and also what is F in the proof?

[fathom flicker]

V' is the set of linear maps from V to F

and F is the field V is defined over

[dense imp]

hm what is meant by a basis of a field?

is that a thing?

[fathom flicker]

every field is a vector space

and in our class F is either C or R, so 1-dimensional

[dense imp]

ok gotcha i think

yeah your argument make sense to me

[fathom flicker]

I feel like it can't be right

I must be missing something

Yes I am

[dense imp]

it doesn't seem that surprising that there would be such a function

[fathom flicker]

this theorem nessecitates that V and the space you're mapping on have the same dimension

so it breaks there

[fathom flicker]

no not at all, but my proof just feels way off

and it is so

any better ideas?

[dense imp]

isn't V' a vector space too

[wild swallow]

i mean its not unique right

like if you set phi(v_1) = 1, you could also set phi(v_2) = whatever

[fathom flicker]

yes

Yeah my proof does not work

[wild swallow]

well it actually does

[fathom flicker]

[wild swallow]

but you just stated some details which arent quite right

[fathom flicker]

the theorem I used is false here

[haughty coyote]

My idea:
||Complete v into a basis then let phi be the projection on the first coordinate||

[polar fossil]

what exactly does this theorem state

[wild swallow]

the uniqueness is false

[fathom flicker]

if v1, ..., vn a basis of V, and w1,... wn a basis of W, then there exists a unique linear map T:V->W such that T(v_i)=w_i

[timid silo]

@fathom flicker

The answer is literally simple

Think harder

Lol

It way easier than you think

[wild swallow]

Blud...

[timid silo]

I figured it out in less than 1 minutes

[haughty coyote]

He's already aware that it fits in 2 lines

[timid silo]

In my head

[haughty coyote]

This isn't a lemme-flex-my-math-speed server

[timid silo]

No i'm just sayings its easier

Hopefully it helps

[fathom flicker]

Okay thanks

now fuck off

[dense imp]

if you have any linear map T that has some vector v1 that isn't in the nullspace then T(v1) = f where f is nonzero right, then wouldn't the linear map 1/f T(v1) = 1

[timid silo]

ok

[wild swallow]

i figured it out in less than -2 years

[haughty coyote]

For anyone familiar with linalg, the answer should be "yeah it's obvious" in 5 seconds so you can process the question

Let's end this

[polar fossil]

that theorem only guarantees uniqueness if they have the same dimensions but if one is lower dimension than the other it should still work right?

[timid silo]

@fathom flicker i'm assuming you're a beginner since you posted a very basic question. i didnt mean to come off as rude, sorry

[polar fossil]

you are not being helpful.

[zenith raft]

who is this clown

[fathom flicker]

@polar fossil They're obviously trolling look at message history, do I need to tag mods or just you

[timid silo]

??

how am i trolling

please elaborate

[haughty coyote]

A newcomer that doesn't quite understand how positive helping works

[zenith raft]

i doubt he knows any linear algebra either

[polar fossil]

no. leave this channel.

[timid silo]

im being falsely accused of trolling

[timid silo]

ok

[dense imp]

@fathom flicker also if you wanna use that theorem you mentioned, could you consider the span(v1) as a 1 dim subspace of V and consider then the linear transformation that the theorem guarantees from span(v1) -> F then extend it into a LA defined on all of V

[haughty coyote]

That's my proof but longer

[timid silo]

it was a theoretical question.

please read the context before using any of my messages against me

[polar fossil]

you can pick where each basis vector ends up, right?

like independently of each other

[dense imp]

i think so?

[wild swallow]

this has a fancy name called the "universal property of vector spaces"

[zenith raft]

that edit changed nothing

[polar fossil]

it actually changed two words

[fathom flicker]

Okay

so albeit with some inspiration from everyone

I have a new proof

Which hopefully works

[zenith raft]

not me

i hope

[fathom flicker]

definitely not

Since v is in V and v !=0 span(V) is a 1D subspace of V with basis v. We can let 1 be a basis of F. Then by previously mentioned theorem there exists a unique linear map phi:span(v)->F such that phi(v)=1. Now we can extend v into a basis of V using w1, ... wn. Then we can extend phi to map all w_i ->0 and we have that phi:V->F has phi(v)=1.

This seems better, does it work?

[wild swallow]

idk why you want to use uniqueness

the question doesnt say that phi needs to be unique

[fathom flicker]

Well I don't need it

but it's included in the theorem statement

[wild swallow]

you can just map v to 1

you dont need that theorem

[fathom flicker]

okay but using this theorem I dont have to justify thats a linear map

[wild swallow]

that theorem is specifically for vector spaces of the same dimension

[fathom flicker]

span(v) and F have the same dimension

[wild swallow]

you should know that for vector spaces, specifying where the basis maps to defines a unique linear map

[polar fossil]

i mean that's exactly what the proof is asking

[wild swallow]

yeah lol

thats pretty much all you have to say

[fathom flicker]

how is that a proof then

let phi(v)=1

done

[polar fossil]

so you clearly can't assume it...

[haughty coyote]

It's my proof yes

[wild swallow]

you choose a basis of V containing v

then map v to 1

thats literally it

[fathom flicker]

why can u map v to 1

[wild swallow]

because its part of the basis

[polar fossil]

this is basically what i was thinking, map one basis vector to 1 and the rest to 0

[fathom flicker]

why can u map any part of the basis to 1

[haughty coyote]

Because there's a map made specifically for that purpose

[wild swallow]

because thats what vector spaces are

a map of vector spaces is uniquely determined by what happens on the basis

[fathom flicker]

so my answer should be "this is what vector spaces are, let phi(v)=1 q.e.d"

[wild swallow]

thats why matrices work

[dense imp]

@fathom flicker what about this:

extend v to a basis for V: {v, v2, v3...v_n}
for some vector w in V let {c1, c2,...c_n} be the unique coefficients of the linear combination of w in terms of the basis: i.e. w = c1(v)+c2(v2)+...c_n(v_n)
define phi(w) be the function where phi(w) = c1
you can verify this is a linear transformation V -> F so it is in V' and it fulfills the property phi(v) = 1

[wild swallow]

it pretty much should be

[fathom flicker]

I think that also works

[fathom flicker]

But Bezier thinks mine works too

so we're all having fun proving this

except Snow

[dense imp]

😄

[wild swallow]

this is all just spelling out the fact that a linear map is determined by its values on a basis

[dense imp]

isnt linear algebra all about expressing the same thing in like a zillion ways

[fathom flicker]

No it is about y=mx+b

[haughty coyote]

We call those projections

[haughty coyote]

That's affine algebra

[wild swallow]

note that phi doesnt need to be 0 elsewhere

[fathom flicker]

okay thank you everyon

especially yungtrapps and layla